1. Summary of Lecture 18 导波条件 图解法求波导模式 边界条件 波导中模式耦合的微扰理论
Coupling constant
周期波导
Phase difference

2. §11.5 Coupled-Mode Solutions
Coupled-mode equations
Reflective wave
Incident wave
Initial conditions:

3. §11.5 Coupled-Mode Solutions
where

4. §11.5 Coupled-Mode Solutions
Under the matching condition

5. §11.5 Coupled-Mode Solutions
z-dependent parts are exponentials with propagation constants
for
has an imaginary part
“forbidden” region
Analogous to the energy gap in semiconductors where the periodic crystal potential causes the electron propagation constants to become complex.
For each l, there has a gap with center frequency

6. §11.5 Coupled-Mode Solutions
“forbidden” gap zone
and
Numerical Example

7. §11.6 Periodic Fibers
How to make a periodic index fiber

8. §11.6 Periodic Fibers Optical reflectors and filters Filter bandwidth
At frequencies near the Bragg frequency, incident mode is strongly reflected; while at frequencies not near Bragg frequency are transmitted with no loss.
Filter bandwidth

9. §11.6 Periodic Fibers
Distributed Feedback Lasers

10. §11.6 Periodic Fibers Consider the condition and infinite
Oscillator condition for DFB
High-gain constant

11. §11.6 Periodic Fibers
Incident and reflected fileds inside an amplifying periodic waveguide

12. §11.7 EO Modulation and Mode Coupling
Optical modulation and switching
(1) Smaller modulation powers (see Eq )
(2) Longer modulation paths (absence of diffraction)
TM  TE mode conversion
dc field
TM mode
Excite a TE mode
Coupled mode equations
Initial conditions:

13. §11.7 EO Modulation and Mode Coupling
Under the matching condition
when
where

14. §11.7 EO Modulation and Mode Coupling
Power exchange between two coupled modes

15. §11.7 EO Modulation and Mode Coupling
EO modulation in a dielectric waveguide

16. §11.8 Directional Coupling
Exchange of power between guided modes of adjacent waveguides is known as directional coupling.
Applications:
Power division, modulation, switching, frequency selection, and polarization selection
Coupled field

17. §11.8 Directional Coupling
Perturbation polarization
Coupled mode equations
Initial conditions:
solutions
Complete power transfer

18. §11.8 Directional Coupling
For
Identical waveguides
Channel waveguides

19. §11.8 Directional Coupling
EO Switch
The directional coupler is designed as:
So that
Now we apply electric field to control the phase such that:
So that

20. §11.8 Directional Coupling
Multiplexing and Demultiplexing

21. §11.8 Directional Coupling
Multiguide directional coupler